एक पिता ने अपने पुत्र से कहा, “n वर्ष पहले मेरी आयु तुम्हारी वर्तमान आयु के बराबर थी। मेरी वर्तमान आयु, तुम्हारी n वर्ष पहले की आयु की चार गुना है”। यदि पिता और पुत्र की वर्तमान आयु का योगफल 130 वर्ष है, तो उनकी आयु में कितना अंतर है?
Read this question in English
A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
(a) 30 years · (b) 32 years · (c) 34 years · (d) 36 years
उत्तर और व्याख्या · explanation in English
Answer: (a) 30 वर्ष
n years ago the father was the son’s present age, so n is the gap between their ages. Using ‘father now = 4 × son n years ago’ gives father : son = 8 : 5, so with a total of 130 they are 80 and 50, a difference of 30 years.
- Let the father’s age be F and the son’s S. ‘n years back I was as old as you are now’: F − n = S, so n = F − S.
- Son’s age n years back = S − n = S − (F − S) = 2S − F.
- F = 4(2S − F) → 5F = 8S → F : S = 8 : 5.
- F + S = 130 → 13 parts = 130 → 1 part = 10, so F = 80 and S = 50.
- Difference = 80 − 50 = 30 years.
- Check: n = 30; the son was 20 thirty years ago, and 4 × 20 = 80.
Remember · ‘I was your present age n years ago’ means n equals the age gap; turn the rest into a ratio.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·